Proof of some supercongruences via the Wilf-Zeilberger method
arXiv:1909.13173 · doi:10.1080/10236198.2020.1854239
Abstract
In this paper, we prove some supercongruences via the Wilf-Zeilberger method. For instance, for any odd prime and positive integer and , we have \begin{align*} \sum_{n=0}^{(p^r-1)/δ} \frac{\left(\frac12\right)^5_n}{n!^5}(10n^2+6n+1)(-4)^n &\equiv\begin{cases}p^{2r}\ \pmod{p^{r+4}} &\tt{if}\ r\leq4, \\0\ \pmod{p^{r+4}} &\tt{if}\ r \geq5. \end{cases} \end{align*}
20 pages. This is a preliminary manuscript. Any comments are welcome